A person goes from P to Q at a speed of 20 km/h. Then he goes from Q to R at a speed of q km/h. Finally the person goes from R to S at a speed of r km/h. The distances from P to Q, Q to R and R to S are equal. If the average speed from P to R is $\frac{280}{11}$ km/h, and the average speed from Q to S is $\frac{112}{3}$ km/h, then what is the value of r?
Answer & explanation
Correct answer: option 1
Let the distance b/w P and Q = Distance b/w Q and R = Distance b/w R and S = D km
We know that,
Speed = \(\frac{Distance}{Time}\)
Time taken from P to Q = \(\frac{D}{20}\) ----(1)
Time taken from Q to R = \(\frac{2D × 3}{112}\)
= \(\frac{3D }{56}\) ----(2)
Time taken from P to R = \(\frac{2D ×11}{280}\)
= \(\frac{11D}{140}\)
Time taken fro Q to R =
On subtracting equation 2 from equation 1,
= \(\frac{11D}{140}\) - \(\frac{D}{20}\)
= \(\frac{11D - 7D}{140}\)
= \(\frac{4D}{140}\)
= \(\frac{D}{35}\)
Time taken from R to S
= \(\frac{3D }{56}\) - \(\frac{D }{35}\)
= \(\frac{49D }{1960}\)
= \(\frac{D }{40}\)
It is given that , Speed of train from R to S = r km/h
According to question,
\(\frac{D }{r}\)= \(\frac{D }{40}\)
r = 40 km/h